There are two main types of waves:

1. Mechanical waves: Require a medium (like air, water, or a solid) to propagate.
   Examples include sound waves and water waves.
2. Electromagnetic waves: Do not require a medium and can travel through a vacuum.
   Examples include light waves and radio waves.

Key Characteristics of Waves

Waves are defined by several measurable properties:

1. Amplitude (A)

   • The amplitude is the maximum displacement of a point on the wave from its rest position.
   • It is a measure of the wave’s energy: larger amplitude = more energy.
   For instance, louder sounds have sound waves with larger amplitudes.

2. Wavelength (λ)

   • The wavelength is the distance between two consecutive points in phase on a wave
     (e.g., crest to crest or trough to trough).
   • It is measured in meters (m).
   For light, wavelength determines the color (e.g., red light has a longer wavelength than blue light).

3. Frequency (f)

   • The frequency is the number of wave cycles that pass a point per second.
   • Measured in hertz (Hz), where 1 Hz = 1 cycle per second.
   High-frequency waves, like gamma rays, carry more energy than low-frequency waves, like radio waves.

4. Frequency (f)

   • The frequency is the number of wave cycles that pass a point per second.
   • Measured in hertz (Hz), where 1 Hz = 1 cycle per second.
   High-frequency waves, like gamma rays, carry more energy than low-frequency waves, like radio waves.

5. Period (T)

   • The period is the time taken for one complete wave cycle to pass a point.
   • Related to frequency by the formula:T=1fT=f1

6. Wave Speed (v)

   • Wave speed is how fast the wave travels through the medium.
   • It is calculated using the formula: v=f×λv=f×λ where vv is wave speed, ff is frequency, and λλ is wavelength.

Types of Waves

1. Transverse Waves

   • The oscillations are perpendicular to the direction of energy transfer.
     Examples: Light waves, water waves, and electromagnetic waves.
   Diagrammatically, transverse waves show crests (highest points) and troughs (lowest points).

2. Longitudinal Waves

   • The oscillations are parallel to the direction of energy transfer.
   
   Examples: Sound waves and compression waves in a spring.
   Longitudinal waves consist of compressions (areas of high particle density) and brarefactions (areas of low particle density).

The Wave Equation

One of the most fundamental relationships in wave physics is:

v=f×λv=f×λ

This equation links the speed of the wave (vv) to its frequency (ff) and wavelength (λλ). It applies to all waves, whether mechanical or electromagnetic.

Example Calculation:

• If a wave has a frequency of 50 Hz and a wavelength of 2 m, its speed is:v=50×2=100 m/s.v=50×2=100m/s.

This equation is indispensable for solving problems related to waves.

Wave Behavior

Waves interact with their surroundings in predictable ways, governed by physical principles:

1. Reflection
   • When a wave hits a surface and bounces back.
     Examples: Echoes are sound waves reflecting off surfaces.
2. Refraction
   • The bending of waves as they pass from one medium to another, caused by a change in speed.
   
   Examples: Light bends when it passes from air into water.
   The degree of refraction depends on the refractive index of the materials.
3. Diffraction
   • The spreading of waves as they pass through a gap or around obstacles.
   • Most pronounced when the gap size is similar to the wavelength.
4. Absorption
   • Some wave energy is absorbed by the medium, converting it to other forms of energy like heat.

Electromagnetic Waves

Electromagnetic waves are a special type of wave that do not require a medium. They are transverse waves consisting of oscillating electric and magnetic fields.

1. Travel at the speed of light (c=3×108 m/sc=3×108m/s) in a vacuum.
2. Organized into the electromagnetic spectrum, which includes (in order of increasing frequency):
   • Radio waves
   • Microwaves
   • Infrared
   • Visible light
   • Ultraviolet
   • X-rays
   • Gamma rays
   Each type of electromagnetic wave has unique properties and applications, from communication (radio waves) to medical imaging (X-rays).

Applications of Wave Theory

Understanding waves allows us to explain and harness their properties in countless technologies and natural phenomena:

• Sound waves: Used in sonar, communication, and ultrasound imaging.
• Light waves: Essential for vision, photography, and fiber-optic communication.
• Electromagnetic waves: Enable wireless communication, medical diagnostics, and even cooking (microwaves).

The principles of wave behavior are fundamental to modern science and engineering, making wave theory one of the most practical topics in physics.